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This paper presents the core ideas of an on-going research exploring teaching approaches for school mathematics with mathematics teachers designing teaching tasks making use of concrete tools and manipulatives. The theories of instrumental genesis and semiotic mediation are used as the main frameworks for the study. A pilot study prior to this on-going research is reported highlighting three tool-based task design principles that are used a guide for the on-going research.

Designing Tool-based Task in the Teaching of School Mathematics